Integrating GPS and GLONASS to accelerate convergence and initialization times of precise point positioning

The main challenge of dual-frequency precise point positioning (PPP) is that it requires about 30 min to obtain centimeter-level accuracy or to succeed in the first ambiguity-fixing. Currently, PPP is generally conducted with GPS only using the ionosphere-free combination. We adopt a single-differenced (SD) between-satellite PPP model to combine the GPS and GLONASS raw dual-frequency carrier phase measurements, in which the GPS satellite with the highest elevation is selected as the reference satellite to form the SD between-satellite measurements. We use a 7-day data set from 178 IGS stations to investigate the contribution of GLONASS observations to both ambiguity-float and ambiguity-fixed SD PPP solutions, in both kinematic and static modes. In ambiguity-fixed PPP, we only attempt to fix GPS integer ambiguities, leaving GLONASS ambiguities as float values. Numerous experimental results show that PPP with GLONASS and GPS requires much less convergence time than that of PPP with GPS alone. For ambiguity-float PPP, the average convergence time can be reduced by 45.9 % from 22.9 to 12.4 min in static mode and by 57.9 % from 40.6 to 17.7 min in kinematic mode, respectively. For ambiguity-fixed PPP, the average time to the first-fixed solution can be reduced by 27.4 % from 21.6 to 15.7 min in static mode and by 42.0 % from 34.4 to 20.0 min in kinematic mode, respectively. Experimental results also show that the less the GPS satellites are used in float PPP, the more significant is the reduction in convergence time when adding GLONASS observations. In addition, on average, more than 4 GLONASS satellites can be observed for most 2-h observation sessions. Nearly, the same improvement in convergence time reduction is achieved for those observations.     

Real-Time Precise Point Positioning (RTPPP) with raw observations and its application in real-time regional ionospheric VTEC modeling

Precise Point Positioning (PPP) is an absolute positioning technology mainly used in post data processing. With the continuously increasing demand for real-time high-precision applications in positioning, timing, retrieval of atmospheric parameters, etc., Real-Time PPP (RTPPP) and its applications have drawn more and more research attention in recent years. This study focuses on the models, algorithms and ionospheric applications of RTPPP on the basis of raw observations, in which high-precision slant ionospheric delays are estimated among others in real time. For this purpose, a robust processing strategy for multi-station RTPPP with raw observations has been proposed and realized, in which real-time data streams and State-Space-Representative (SSR) satellite orbit and clock corrections are used. With the RTPPP-derived slant ionospheric delays from a regional network, a real-time regional ionospheric Vertical Total Electron Content (VTEC) modeling method is proposed based on Adjusted Spherical Harmonic Functions and a Moving-Window Filter. SSR satellite orbit and clock corrections from different IGS analysis centers are evaluated. Ten globally distributed real-time stations are used to evaluate the positioning performances of the proposed RTPPP algorithms in both static and kinematic modes. RMS values of positioning errors in static/kinematic mode are 5.2/15.5, 4.7/17.4 and 12.8/46.6 mm, for north, east and up components, respectively. Real-time slant ionospheric delays from RTPPP are compared with those from the traditional Carrier-to-Code Leveling (CCL) method, in terms of function model, formal precision and between-receiver differences of short baseline. Results show that slant ionospheric delays from RTPPP are more precise and have a much better convergence performance than those from the CCL method in real-time processing. 30 real-time stations from the Asia-Pacific Reference Frame network are used to model the ionospheric VTECs over Australia in real time, with slant ionospheric delays from both RTPPP and CCL methods for comparison. RMS of the VTEC differences between RTPPP/CCL method and CODE final products is 0.91/1.09 TECU, and RMS of the VTEC differences between RTPPP and CCL methods is 0.67 TECU. Slant Total Electron Contents retrieved from different VTEC models are also validated with epoch-differenced Geometry-Free combinations of dual-frequency phase observations, and mean RMS values are 2.14, 2.33 and 2.07 TECU for RTPPP method, CCL method and CODE final products, respectively. This shows the superiority of RTPPP-derived slant ionospheric delays in real-time ionospheric VTEC modeling.     

Assessment of correct fixing rate for precise point positioning ambiguity resolution on a global scale

Ambiguity resolution (AR) for a single receiver has been a popular topic in Global Positioning System (GPS) recently. Ambiguity-resolution methods for precise point positioning (PPP) have been well documented in recent years, demonstrating that it can improve the accuracy of PPP. However, users are often concerned about the reliability of ambiguity-fixed PPP solution in practical applications. If ambiguities are fixed to wrong integers, large errors would be introduced into position estimates. In this paper, we aim to assess the correct fixing rate (CFR), i.e., number of ambiguities correctly fixing to the total number of ambiguities correctly and incorrectly fixing, for PPP user ambiguity resolution on a global scale. A practical procedure is presented to evaluate the CFR of PPP user ambiguity resolution. GPS data of the first 3 days in each month of 2010 from about 390 IGS stations are used for experiments. Firstly, we use GPS data collected from about 320 IGS stations to estimate global single-differenced (SD) wide-lane and narrow-lane satellite uncalibrated phase delays (UPDs). The quality of UPDs is evaluated. We found that wide-lane UPD estimates have a rather small standard deviation (Std) between 0.003 and 0.004 cycles while most of Std of narrow-lane estimates are from 0.01 to 0.02 cycles. Secondly, many experiments have been conducted to investigate the CFR of integer ambiguity resolution we can achieve under different conditions, including reference station density, observation session length and the ionospheric activity. The results show that the CFR of PPP can exceed 98.0 % with only 1 h of observations for most user stations. No obvious correlation between the CFR and the reference station density is found. Therefore, nearly homogeneous CFR can be achieved in PPP AR for global users. At user end, higher CFR could be achieved with longer observations. The average CFR for 30-min, 1-h, 2-h and 4-h observation is 92.3, 98.2, 99.5 and 99.7 %, respectively. In order to get acceptable CFR, 1 h is a recommended minimum observation time. Furthermore, the CFR of PPP can be affected by diurnal variation and geomagnetic latitude variation in the ionosphere. During one day at the hours when rapid ionospheric variations occur or in low geomagnetic latitude regions where equatorial electron density irregularities are produced relatively frequently, a significant degradation of the CFR is demonstrated.     

基于原始观测值的单频精密单点定位算法

研究了一种基于GPS原始观测值的单频PPP算法。该算法通过增加电离层延迟先验信息、空间和时间约束的虚拟观测方程,将电离层延迟当作未知参数与其他定位参数一并进行估计来高效修正电离层延迟误差。通过使用全球178个IGS站1d的实测数据对本算法的收敛速度、定位精度和电离层VTEC的精度进行检验与分析。结果表明,该算法的收敛速度和稳定性均得到了改善,其静态单频单天PPP解的精度可达2~3cm、模拟动态单频单天PPP解的精度可达2~3dm,并且单频PPP与双频PPP提取的电离层总电子含量平均偏差小于5个TECU,可作为一种附属定位产品使用。     

估计接收机差分码偏差的GPS/BDS非组合精密单点定位模型

在传统多系统非差非组合精密单点定位（precise point positioning,PPP）模型中,电离层延迟会吸收部分接收机码硬件延迟,其估计值可能为负数。提出了一种估计接收机差分码偏差（differential code bias,DCB）参数的GPS（Global Positioning System）/BDS（BeiDou Navigation Satellite System）非组合PPP模型,将每个系统第1个频率上的接收机码硬件延迟约束为零,对接收机DCB进行参数估计,达到了分离电离层延迟和接收机码硬件延迟的目的,降低了接收机钟差和电离层延迟的相关程度。利用4个多星座实验（multi-GNSS experiment,MGEX）跟踪站的GPS/BDS数据进行了静态和动态PPP试验,结果表明,与不估计DCB参数的PPP模型相比,采用估计DCB参数PPP模型后,静态模式下定位精度和收敛速度平均提高了29.3%和29.8%,动态模式下定位精度和收敛速度平均提高了15.7%和21.6%。     

Real-time precise point positioning regional augmentation for large GPS reference networks

An increasing number of GNSS reference stations are installed around the world to provide real-time precise positioning services. In most of the current services, a full network solution is required for the precise determination of biases. Such a network solution is time consuming and difficult to achieve for very large regions such as Europe or China. Therefore, we developed a multi-layer processing scheme for precise point positioning (PPP) regional augmentation to avoid processing large networks. Furthermore, we use L1 and L2 raw observations and estimate atmospheric delays, which were properly constrained to the atmospheric corrections derived from the reference stations. Therefore, inaccurate representation of atmospheric delays due to temporal and/or spatial atmospheric fluctuations in the processing can be compensated. The proposed scheme of PPP regional augmentation was implemented into the operational real-time PPP service system at GFZ for validation. The real-time orbit and clock corrections, the uncalibrated phase delays, and regional augmentation corrections are generated by this system. The augmentation corrections from the regional network are investigated and the positioning performance in terms of positioning accuracy and time for fixed solution is demonstrated in real-time. Our results indicate that a reliable fixing is possible after 5 s on average. The positioning accuracy is about 12, 10, and 25 mm in east, north, and vertical direction, respectively.     

Joint estimation of GPS/BDS real-time clocks and initial results

We present the joint estimation model for Global Positioning System/BeiDou Navigation Satellite System (GPS/BDS) real-time clocks and present the initial satellite clock solutions determined from 106 stations of the international GNSS service multi-GNSS experiment and the BeiDou experimental tracking stations networks for 1 month in December, 2012. The model is shown to be efficient enough to have no practical computational limit for producing 1-Hz clock updates for real-time applications. The estimated clocks were assessed through the comparison with final clock products and the analysis of post-fit residuals. Using the estimated clocks and corresponding orbit products (GPS ultra-rapid-predicted and BDS final orbits), the root-mean-square (RMS) values of coordinate differences from ground truth values are around 1 and 2–3 cm for GPS-only and BDS-only daily mean static precise point positioning (PPP) solutions, respectively. Accuracy of GPS/BDS combined static PPP solutions falls in between that of GPS-only and BDS-only PPP results, with RMS values approximately 1–2 cm in all three components. For static sites, processed in the kinematic PPP mode, the daily RMS values are normally within 4 and 6 cm after convergence for GPS-only and BDS-only results, respectively. In contrast, the combined GPS/BDS kinematic PPP solutions show higher accuracy and shorter convergence time. Additionally, the BDS-only kinematic PPP solutions using clock products derived from the proposed joint estimation model were superior compared to those computed using the single-system estimation model.     

Simultaneous estimation of GLONASS pseudorange inter-frequency biases in precise point positioning using undifferenced and uncombined observations

GLONASS precise point positioning (PPP) performance is affected by the inter-frequency biases (IFBs) due to the application of frequency division multiple access technique. In this contribution, the impact of GLONASS pseudorange IFBs on convergence performance and positioning accuracy of GLONASS-only and GPS + GLONASS PPP based on undifferenced and uncombined observation models is investigated. Through a re-parameterization process, the following four pseudorange IFB handling schemes were proposed: neglecting IFBs, modeling IFBs as a linear or quadratic polynomial function of frequency number, and estimating IFBs for each GLONASS satellite. One week of GNSS observation data from 132 International GNSS Service stations was selected to investigate the contribution of simultaneous estimation of GLONASS pseudorange IFBs on GLONASS-only and combined GPS + GLONASS PPP in both static and kinematic modes. The results show that considering IFBs can speed up the convergence of PPP using GLONASS observations by more than 20%. Apart from GLONASS-only kinematic PPP, the positioning accuracy of GLONASS-only and GPS + GLONASS PPP is comparable among the four schemes. Overall, the scheme of estimating IFBs for each GLONASS satellite outperforms the other schemes in both convergence time reduction and positioning accuracy improvement, which indicates that the GLONASS IFBs may not strictly obey a linear or quadratic function relationship with the frequency number.     

Multi-GNSS precise point positioning (MGPPP) using raw observations

A joint-processing model for multi-GNSS (GPS, GLONASS, BDS and GALILEO) precise point positioning (PPP) is proposed, in which raw code and phase observations are used. In the proposed model, inter-system biases (ISBs) and GLONASS code inter-frequency biases (IFBs) are carefully considered, among which GLONASS code IFBs are modeled as a linear function of frequency numbers. To get the full rank function model, the unknowns are re-parameterized and the estimable slant ionospheric delays and ISBs/IFBs are derived and estimated simultaneously. One month of data in April, 2015 from 32 stations of the International GNSS Service (IGS) Multi-GNSS Experiment (MGEX) tracking network have been used to validate the proposed model. Preliminary results show that RMS values of the positioning errors (with respect to external double-difference solutions) for static/kinematic solutions (four systems) are 6.2 mm/2.1 cm (north), 6.0 mm/2.2 cm (east) and 9.3 mm/4.9 cm (up). One-day stabilities of the estimated ISBs described by STD values are 0.36 and 0.38 ns, for GLONASS and BDS, respectively. Significant ISB jumps are identified between adjacent days for all stations, which are caused by the different satellite clock datums in different days and for different systems. Unlike ISBs, the estimated GLONASS code IFBs are quite stable for all stations, with an average STD of 0.04 ns over a month. Single-difference experiment of short baseline shows that PPP ionospheric delays are more precise than traditional leveling ionospheric delays.     

A reference station-based GNSS computing mode to support unified precise point positioning and real-time kinematic services

Currently, the GNSS computing modes are of two classes: network-based data processing and user receiver-based processing. A GNSS reference receiver station essentially contributes raw measurement data in either the RINEX file format or as real-time data streams in the RTCM format. Very little computation is carried out by the reference station. The existing network-based processing modes, regardless of whether they are executed in real-time or post-processed modes, are centralised or sequential. This paper describes a distributed GNSS computing framework that incorporates three GNSS modes: reference station-based, user receiver-based and network-based data processing. Raw data streams from each GNSS reference receiver station are processed in a distributed manner, i.e., either at the station itself or at a hosting data server/processor, to generate station-based solutions, or reference receiver-specific parameters. These may include precise receiver clock, zenith tropospheric delay, differential code biases, ambiguity parameters, ionospheric delays, as well as line-of-sight information such as azimuth and elevation angles. Covariance information for estimated parameters may also be optionally provided. In such a mode the nearby precise point positioning (PPP) or real-time kinematic (RTK) users can directly use the corrections from all or some of the stations for real-time precise positioning via a data server. At the user receiver, PPP and RTK techniques are unified under the same observation models, and the distinction is how the user receiver software deals with corrections from the reference station solutions and the ambiguity estimation in the observation equations. Numerical tests demonstrate good convergence behaviour for differential code bias and ambiguity estimates derived individually with single reference stations. With station-based solutions from three reference stations within distances of 22–103 km the user receiver positioning results, with various schemes, show an accuracy improvement of the proposed station-augmented PPP and ambiguity-fixed PPP solutions with respect to the standard float PPP solutions without station augmentation and ambiguity resolutions. Overall, the proposed reference station-based GNSS computing mode can support PPP and RTK positioning services as a simpler alternative to the existing network-based RTK or regionally augmented PPP systems.     

GLONASS phase bias estimation and its PPP ambiguity resolution using homogeneous receivers

Integer ambiguity resolution (IAR) appreciably improves the position accuracy and shortens the convergence time of precise point positioning (PPP). However, while many studies are limited to GPS, there is a need to investigate the performance of GLONASS PPP ambiguity resolution. Unfortunately, because of the frequency-division multiple-access strategy of GLONASS, GLONASS PPP IAR faces two obstacles. First, simultaneously observed satellites operate at different wavelengths. Second and most importantly, distinct inter-frequency bias (IFB) exists between different satellites. For the former, we adopt an undifferenced method for uncalibrated phase delay (UPD) estimation and proposed an undifferenced PPP IAR strategy. We select a set of homogeneous receivers with identical receiver IFB to perform UPD estimation and PPP IAR. The code and carrier phase IFBs can be absorbed by satellite wide-lane and narrow-lane UPDs, respectively, which is in turn consistent with PPP IAR using the same type of receivers. In order to verify the method, we used 50 stations to generate satellite UPDs and another 12 stations selected as users to perform PPP IAR. We found that the GLONASS satellite UPDs are stable in time and space and can be estimated with high accuracy and reliability. After applying UPD correction, 91 % of wide-lane ambiguities and 99 % of narrow-lane ambiguities are within (?0.15, +0.15) cycles of the nearest integer. After ambiguity resolution, the 2-hour static PPP accuracy improves from (0.66, 1.42, 1.55) cm to (0.38, 0.39, 1.39) cm for the north, east, and up components, respectively.     

BDS/GPS精密单点定位收敛时间与定位精度的比较

采用武汉大学卫星导航定位技术研究中心发布的北斗精密卫星轨道和钟差,在TriP 2.0软件的基础上实现了BDS PPP定位算法,并利用大量实测数据进行了BDS/GPS静态PPP和动态PPP浮点解试验。结果表明,BDS静态PPP的收敛时间约为80min,动态PPP的收敛时间为100min;对于3h的观测数据,静态PPP收敛后定位精度优于5cm,动态PPP收敛后水平方向优于8cm,高程方向约12cm;与GPS PPP类似,东分量上定位精度较北分量稍差。当前由于BDS的全球跟踪站有限,精密轨道和钟差精度不如GPS,因此BDS PPP的收敛时间较GPS长,但收敛后可实现厘米至分米级的绝对定位。     

Rapid re-convergences to ambiguity-fixed solutions in precise point positioning

Integer ambiguity resolution at a single receiver can be achieved if the fractional-cycle biases are separated from the ambiguity estimates in precise point positioning (PPP). Despite the improved positioning accuracy by such integer resolution, the convergence to an ambiguity-fixed solution normally requires a few tens of minutes. Even worse, these convergences can repeatedly occur on the occasion of loss of tracking locks for many satellites if an open sky-view is not constantly available, consequently totally destroying the practicability of real-time PPP. In this study, in case of such re-convergences, we develop a method in which ionospheric delays are precisely predicted to significantly accelerate the integer ambiguity resolution. The effectiveness of this method consists in two aspects: first, wide-lane ambiguities can be rapidly resolved using the ionosphere-corrected wide-lane measurements, instead of the noisy Melbourne–Wübbena combination measurements; second, narrow-lane ambiguity resolution can be accelerated under the tight constraints derived from the ionosphere-corrected unambiguous wide-lane measurements. In the test at 90 static stations suffering from simulated total loss of tracking locks, 93.3 and 95.0% of re-convergences to wide-lane and narrow-lane ambiguity resolutions can be achieved within five epochs of 1-Hz measurements, respectively, even though the time latency for the predicted ionospheric delays is up to 180 s. In the test at a mobile van moving in a GPS-adverse environment where satellite number significantly decreases and cycle slips frequently occur, only when the predicted ionospheric delays are applied can the rate of ambiguity-fixed epochs be dramatically improved from 7.7 to 93.6% of all epochs. Therefore, this method can potentially relieve the unrealistic requirement of a continuous open sky-view by most PPP applications and improve the practicability of real-time PPP.     

多GNSS系统组合PPP定位精度评估

采用MGEX网提供的GPS、GLONASS、BDS、GALILEO四系统双频观测数据,以CODE、GBM、WUM、GRG精密产品进行了静/准动态模式下多系统组合无电离层延迟PPP浮点解与整数钟法固定解实验。结果表明多系统的组合提升了定位精度,尤其是GLONASS的加入效果最明显,CODE与GBM产品的解算精度优于WUM、GRG产品。部分模糊度固定相比全模糊度固定的效果显著,模糊度固定明显缩短了PPP收敛时间,在静态模式下相对浮点解精度提升10%以内,动态模式下E方向与U方向精度提升效果最好。     

Integrating GPS and BDS to shorten the initialization time for ambiguity-fixed PPP

The main challenge of ambiguity resolution in precise point positioning (PPP) is that it requires 30 min or more to succeed in the first fixing of ambiguities. With the full operation of the BeiDou (BDS) satellite system in East Asia, it is worthwhile to investigate the performance of GPS + BDS PPP ambiguity resolution, especially the improvements of the initial fixing time and ambiguity-fixing rate compared to GPS-only solutions. We estimated the wide- and narrow-lane fractional-cycle biases (FCBs) for BDS with a regional network, and PPP ambiguity resolution was carried out at each station to assess the contribution of BDS. The across-satellite single-difference (ASSD) GPS + BDS combined ambiguity-fixed PPP model was used, in which the ASSD is applied within each system. We used a two-day data set from 48 stations. For kinematic PPP, the percentage of fixing within 10 min for GPS only (Model A) is 17.6 %, when adding IGSO and MEO of BDS (Model B), the percentage improves significantly to 42.8 %, whereas it is only 23.2 % if GEO is added (Model C) due to the low precision of GEO orbits. For static PPP, the fixing percentage is 32.9, 53.3 and 28.0 % for Model A, B and C, respectively. In order to overcome the limitation of the poor precision of GEO satellites, we also used a small network of 10 stations to analyze the contribution of GEO satellites to kinematic PPP. We took advantage of the fact that for stations of a small network the GEO satellites appear at almost the same direction, such that the GEO orbit error can be absorbed by its FCB estimates. The results show that the percentage of fixing improves from 39.5 to 57.7 % by adding GEO satellites.     

Ambiguity resolved precise point positioning with GPS and BeiDou

This paper focuses on the contribution of the global positioning system (GPS) and BeiDou navigation satellite system (BDS) observations to precise point positioning (PPP) ambiguity resolution (AR). A GPS + BDS fractional cycle bias (FCB) estimation method and a PPP AR model were developed using integrated GPS and BDS observations. For FCB estimation, the GPS + BDS combined PPP float solutions of the globally distributed IGS MGEX were first performed. When integrating GPS observations, the BDS ambiguities can be precisely estimated with less than four tracked BDS satellites. The FCBs of both GPS and BDS satellites can then be estimated from these precise ambiguities. For the GPS + BDS combined AR, one GPS and one BDS IGSO or MEO satellite were first chosen as the reference satellite for GPS and BDS, respectively, to form inner-system single-differenced ambiguities. The single-differenced GPS and BDS ambiguities were then fused by partial ambiguity resolution to increase the possibility of fixing a subset of decorrelated ambiguities with high confidence. To verify the correctness of the FCB estimation and the effectiveness of the GPS + BDS PPP AR, data recorded from about 75 IGS MGEX stations during the period of DOY 123-151 (May 3 to May 31) in 2015 were used for validation. Data were processed with three strategies: BDS-only AR, GPS-only AR and GPS + BDS AR. Numerous experimental results show that the time to first fix (TTFF) is longer than 6 h for the BDS AR in general and that the fixing rate is usually less than 35 % for both static and kinematic PPP. An average TTFF of 21.7 min and 33.6 min together with a fixing rate of 98.6 and 97.0 % in static and kinematic PPP, respectively, can be achieved for GPS-only ambiguity fixing. For the combined GPS + BDS AR, the average TTFF can be shortened to 16.9 min and 24.6 min and the fixing rate can be increased to 99.5 and 99.0 % in static and kinematic PPP, respectively. Results also show that GPS + BDS PPP AR outperforms single-system PPP AR in terms of convergence time and position accuracy.     

BDS/Galileo四频精密单点定位模型性能分析与比较

北斗卫星导航系统和Galileo卫星系统都可以提供4个频率信号上的服务。本文通过与双频无电离层模型（DF）比较,评估分析了4种BDS/Galileo四频PPP模型性能,即四频无电离层双组合模型（QF1）、四频无电离层组合模型（QF2）、四频非差非组合模型（QF3）和附加电离层约束四频非差非组合模型（QF4）,同时通过等价性原则理论上证明了QF1、QF2、QF3模型的等价性。此外,用1个月参考站的静态数据和1组动态数据分析了四频静态,仿动态和动态PPP性能。试验结果表明,BDS-3 B1C和B2a新频点伪距噪声要略大于B1I和B3I信号,Galileo卫星4个频率上的伪距噪声相差并不明显。对于静态和仿动态PPP模型,QF1、QF2和QF3模型定位性能基本上一致。通过附加外部电离层约束,四频PPP模型性能受到影响,BDS（BDS-2+BDS-3）静态QF4模型相比于QF1、QF2和QF3模型平均收敛时间分别减少了4.4%、4.4%和5.4%,Galileo静态Q4模型平均收敛时间相比于Q3模型增加了16.8 min。对于动态PPP,四频PPP模型相比于双频PPP性能得到提升显著,相比于QF1模型,BDS和Galileo单系统QF4模型三维定位精度分别提高了11.4%和31.4%。BDS/Galileo双系统PPP性能要优于单系统PPP。     

Spatial–temporal characteristic of BDS phase delays and PPP ambiguity resolution with GEO/IGSO/MEO satellites

GPS precise point positioning (PPP) ambiguity resolution (AR) can improve the positioning accuracy and shorten the convergence time. However, for the BeiDou Satellite Navigation System (BDS), the problems of satellite-induced code bias, imperfections in the error models and the inadequate accuracy of orbit products limit the applications of the BDS PPP AR system, which requires more than 6 h to achieve the first ambiguity-fixed solution. In this study, the accuracy of a wide-lane (WL) uncalibrated phase delay (UPD) is improved after careful consideration of the code bias and multipath. Meanwhile, the accuracy of the BDS float ambiguity is also improved by multi-GNSS fusion and improved precise orbit and clock products, which are critical for high-quality narrow-lane (NL) UPD estimations. With three tracking networks of different scales, including Hong Kong, the Crustal Movement Observation Network of China (CMONOC) and the multi-GNSS experiment (MGEX) networks, the spatial–temporal characteristics of WL and NL UPDs for BDS GEO/IGSO/MEO satellites are analyzed, and the PPP AR is performed. Numerous results show that WL and NL UPDs with a standard deviation (STD) of less than 0.15 cycles can be achieved for BDS GEO satellites, while a STD of less than 0.1 cycles can be obtained for IGSO and MEO satellites. With the precise UPD estimation, for the first time, the BDS PPP rapid ambiguity resolution for GEO/IGSO/MEO satellites is achieved. We found that the average time to first fix (TTFF) of the BDS PPP AR is shortened significantly, to approximately 40 min for Hong Kong and the CMONOC, while the TTFF was 57.4 min for the MGEX networks. With ambiguity resolution, the accuracy of the daily BDS PPP in the east, north and vertical directions improves from 1.74 cm, 1.08 cm, and 5.52 cm to 0.72 cm, 0.54 cm, and 3.21 cm for the Hong Kong network, 2.24 cm, 2.31 cm, and 5.64 cm to 1.18 cm, 0.79 cm, and 3.30 cm for the CMONOC, and 2.71 cm, 1.80 cm, and 6.00 cm to 1.58 cm, 1.15 cm, and 4.33 cm for the MGEX networks. Significant improvement is also achieved for kinematic PPP, with improvements of 40.41%, 34.33% and 37.17% in the east, north and vertical directions for the MGEX networks, respectively.     

GNSS精密单点定位技术及应用进展

综合分析讨论了GNSS精密单点定位(PPP)技术及应用的最新进展。重点对GNSS精密单点定位实数解、固定解、实时精密单点定位、PPP-RTK和多频多系统精密单点定位等5个方面的核心关键技术和实现方法进行了总结和讨论。结合PPP技术的特点和优势,论述了PPP在低轨卫星定轨、地震、对流层和电离层等方面的典型应用。针对多频多系统GNSS的最新发展动态,展望了PPP技术今后的发展趋势,并指出了精密单点定位技术和推广应用还有待进一步研究的问题。     

Multifrequency algorithms for precise point positioning: MAP3

We present the new MAP3 algorithms to perform static precise point positioning (PPP) from multifrequency and multisystem GNSS observations. MAP3 represents a two-step strategy in which the least squares theory is applied twice to estimate smoothed pseudo-distances, initial phase ambiguities, and slant ionospheric delay first, and the absolute receiver position and its clock offset in a second adjustment. Unlike the classic PPP technique, in our new approach, the ionospheric-free linear combination is not used. The combination of signals from different satellite systems is accomplished by taking into account the receiver inter-system bias. MAP3 has been implemented in MATLAB and integrated within a complete PPP software developed on site and named PCube. We test the MAP3 performance numerically and contrast it with other external PPP programs. In general, MAP3 positioning accuracy with low-noise GPS dual-frequency observations is about 2.5 cm in 2-h observation periods, 1 cm in 10 h, and 7 mm after 1 day. This means an improvement in the accuracy in short observation periods of at least 7 mm with respect to the other PPP programs. The MAP3 convergence time is also analyzed and some results obtained from real triple-frequency GPS and GIOVE observations are presented.